Oscillating probe AFM uses a probe drive signal to generate substantially repetitive oscillatory motion of the AFM probe, which motion the AFM detects; but this motion is altered as a result in part of the AFM probe's sensing tip repeatedly approaching to and retracting from and/or making and breaking contact with the surface of the sample under study.
In this document the terms interaction and force are used interchangeably. In this document, tip-sample interaction covers conditions in which the tip and the sample are close enough for there to be between them detectably strong attractive forces such as van der Waals forces and/or adhesive forces (as described for example in “Interpretation of force curves in force microscopy” by N. A. Burnham et. al. in Nanotechnology Volume 4, 1993, pp 64-80) in the absence or in the presence of detectably strong repulsive contact mechanics forces as described for example by contact mechanics theory of Sneddon (for example in “The relation between load and penetration in the axisymmetric boussinesque problem for a punch of arbitrary profile”, Ian N. Sneddon, International Journal of Engineering Science, volume 3, pp. 47-57. Pergamon Press 1965) and/or contact mechanics theory of Hertz (for example in “Contact Mechanics” by K. L. Johnson, Cambridge University Press 1985) and/or any other contact mechanics theory such as the Johnson-Kendall-Roberts (JKR) theory and the Derjaguin-Muller-Toporov (DMT) theory (Ibid., N. A. Burnham et. al.) Therefore, unless specifically stated otherwise, tip-sample interaction (or force) including intermittent includes any one or more of 1) exclusively attractive forces including possibly adhesive forces, 2) predominantly attractive forces with repulsive forces also present, 3) predominantly repulsive forces with attractive forces possibly including adhesive forces also present, and 4) the transitions between any two or any three of 1, 2, and 3 in this sentence. Furthermore, intermittent contact is used interchangeably with intermittent interaction. Therefore, similarly, intermittent contact may include attractive forces and/or adhesive forces and/or repulsive forces and transitions between them as discussed above in the context of intermittent interaction.
An example of prior art atomic force microscope (AFM) is illustrated in FIG. 1. In an AFM, a microfabricated probe also may be referred to as a probe and/or an AFM probe and includes an integrated sharp tip that also may be referred to as a tip, an AFM tip, an AFM probe tip, and/or a probe tip. The AFM probe tip interacts with its surroundings, which include of main interest the sample surface or immediate sub-surface as the AFM implements either one or both types of raster-scanning motion and approach-retract motion (including AFM force spectroscopy which involves one or more cycles of approach and retract) between the probe and the sample surface. FIG. 1 illustrates probe 4P and probe tip 6P and sample 10 in prior art. Raster-scanning motion is usually in a plane called the xy plane substantially parallel to the sample stage, a usually flat stage on which the sample rests. FIG. 1 illustrates sample stage 800P in prior art. The sample stage is usually parallel to the horizontal plane, but need not necessarily be so. Approach-retract motion including in AFM force spectroscopy is usually in a direction usually called the z direction substantially perpendicular to the xy plane. Raster-scanning is implemented with an actuator usually called the xy-actuator and approach-retract motion is usually implemented using an actuator usually called the z-actuator. FIG. 1 illustrates xy-actuator 744P and z-actuator 700P in some prior art. Raster-scanning and approach-retract motion are implemented by either holding the sample at a fixed position while moving the probe, or by holding the probe (which may be an oscillating probe) at one location while moving the sample. It is possible to have raster-scanning concurrently with approach-retract and force spectroscopy.
The AFM probe is typically a microfabricated cantilever beam, and the tip, including a usually nanometer-scale-sharp apex, is integrated into or attached to the free end of the cantilever probe opposite the clamped end of the probe. AFM probes with geometry different from the cantilever beam have also proven useful, but the dominant, most widely used shape has remained the cantilever beam.
In oscillating probe AFM modes, also referred to as dynamic (or AC) AFM modes, such as amplitude modulation AFM (AM-AFM), or frequency modulation AFM (FM-AFM), or torsion resonance mode AFM (TR-AFM), the probe is intentionally driven into mechanical oscillations, (i.e., oscillatory movement), which in the absence of tip-sample interaction are substantially, though not necessarily strictly, time periodic. These oscillations are indicated as “A” and the adjacent curved double-headed arrow in FIG. 1.
This movement is usually induced by applying a signal called the probe drive signal 5P directly or indirectly to the said probe. For example, the probe drive signal may be applied to a mechanical actuator such as a piezoelectric device or a quartz crystal which is in turn mechanically, i.e., via contact, coupled to the clamped base of a cantilever probe and drives the said probe into motion. Alternatively, the probe drive signal may be applied directly to the probe in the form of a modulated electromagnetic signal which brings about the said probe motion by generating thermally-induced stresses in the body of the probe (see, e.g., Scanning attractive force microscope using photothermal vibration, N. Umeda et. al., Journal of Vacuum Science and Technology B. April 1991; High efficiency laser photothermal excitation of microcantilever vibrations in air and liquids, D. Kiracofe, et. al., Review of Scientific Instruments; volume 82, 013702 (2011); and Photothermal excitation for improved cantilever drive performance in tapping mode atomic force microscopy, A. Labuda, et. al, in Microscopy and Analysis, SPM Supplement, March/April 2014). Alternatively, the probe drive signal may be applied to an inductive coil, thus generating a time-varying magnetic field which, when coupled to a magnetic coating on the probe, generates the said probe oscillatory motion.
In oscillating probe mode AFM, usually each of the single or multiple frequencies prominent or dominant in the frequency spectrum of the probe drive signal is chosen to be at or near to a mechanical resonance frequency associated with the probe's normal modes of oscillation; i.e., an eigenfrequency of the probe. One exception is peak-force tapping mode AFM (U.S. Pat. No. 8,739,309 B2). The eigenfrequencies that characterize the normal modes of a given probe are in turn determined in-part by the probe's geometry and material composition. In general, the probe drive signal generates probe movement of different types, which include torsion, bending, and rotation of the probe. In the case of a cantilever probe, these include but are not limited to torsion about the cantilever's long axis; bending along the cantilever's long axis; and rotation about an axis along the width of the cantilever at or near its clamped base. In general, as of this writing the most widely used probe drive signal is a single frequency sinusoid; however, multi-frequency probe drive signals have also been developed. See, e.g., “The emergence of multifrequency force microscopy”, Ricardo Garcia and Elena T. Herruzo, Nature Nanotechnology, published online 1 Apr. 2012; and 6th Multi-frequency AFM Conference, 30 Mar.-1 Apr. 2016, Madrid Spain; and “Bimodal Dual AC Imaging”, Application Note 09, Asylum Research, a division of Oxford Instruments; and “Band excitation method applicable to scanning probe microscopy”, U.S. Pat. No. 7,775,086 B2.
A signal called the probe response signal 59P (FIG. 1) may include information about the tip-sample interaction as it does when the oscillating probe's sensing tip 6P makes intermittent contact with the surface of the sample 10.
The probe response signal 59P characterizes the response of the probe 4P to one or more of 1) the probe drive signal 5P; 2) the interaction of the probe's sensing tip 6P with the sample which is herein called the tip-sample interaction; and 3) the interaction of the probe 4P and its tip 6P with its surroundings minus the sample which includes all sources of noise and the ambient fluid (gaseous or liquid) which engulfs the probe 4P and its tip 6P.
Feedback in Oscillating Probe AFM
In this document, unless otherwise noted, any reference to totality of probe movement, totality of probe oscillations, probe oscillations whole, and the whole of probe movement, is to be understood in the context of such movement and such oscillations as encoded in the probe response signal and subject to inherent or intentionally introduced limitations of the detection and signal processing scheme used, especially viz. frequency selectivity. Therefore, depending on the probe and depending on the nature and the functional details of the detector and the detection scheme and signal processing used, including for example the Detector 20P and Signal Conditioner and Processor 30P in FIG. 1, the said movement and the said oscillation or oscillations qualified by the word “whole” and/or by the word “totality” may be the movement and/or the oscillation or oscillations of a location on the probe and/or of a multiplicity of locations on the probe and/or possibly though not necessarily of the entire probe. Furthermore, depending on the composition of the probe drive signal (e.g., single-frequency versus multi-frequency) and depending on the manner in which the probe response signal is constructed, the said movement and the said oscillation or oscillations qualified by the word “whole” and/or by the word “totality” may be the movement and/or oscillation or oscillations at a single frequency or at multiple frequencies or at a continuous band of frequencies.
In general, and in summary, closed-loop or feedback control of tip-sample interaction in oscillating probe AFM is usually implemented by first obtaining a probe response signal 59P indicative of the AFM probe movement; then by constructing from the probe response signal another signal 959P which is the input to a feedback loop (feedback input signal); then by comparing the feedback input signal with a setpoint signal 375P and thereby generating an error signal 405P which measures how far the feedback input signal is from the setpoint signal, and which measurement is usually made by subtracting the value of the setpoint signal 405P from the value of feedback input signal 959P or vice-versa; then by implementing a control algorithm, for example by implementing any one or more of proportional, integral, and differential (PID) gains, on the error signal 405P thereby generating a feedback output signal 1089P which is usually amplified (high voltage or HV Gains 490P) and possibly filtered or otherwise suitably processed further but not necessarily in that order before it is applied to one or more actuators 700P whose collective action is meant to reduce, ideally to zero, the said error signal 405P.
The word actuator is used herein in the context of the discipline of automatic control. Therefore, the action of the actuator may be mechanical in nature, as is the case for a piezoelectric actuator which affects movement and thereby spatially relocates an object such as the probe or the sample. Indeed, the AFM's controlling actuators frequently consist of one or more piezoelectric elements the collective action of which is intended to reposition the probe or the sample in real-time or near real-time so as to adjust the probe-sample distance, thus rendering the desired result of reducing, ideally to zero, the said error signal. The AFM image based on this feedback output signal is usually referred to as the “topography image” or “height image”, and is the most commonly captured, analyzed, and presented and published type of AFM image. The action of the actuator may also be non-mechanical; for example the actuator may change the strength or polarity of an applied electrical potential difference or voltage; or the actuator may change a single frequency or multiple component frequencies or the amplitude or the phase of the AFM probe drive signal; or the actuator may adjust the AFM control parameters including the setpoint signal and any one or more of proportional gain, integral gain, or differential gain. Actuators may control probe and/or sample positioning, and they may also control signals and control parameters. When the latter is the case, then the actuator is not necessarily a positioning device such as a piezoelectric element; rather, it may be one or more electrical elements the combined actions of which bring about a change, for example, in a control parameter such as a gain or a setpoint, or for example in a probe drive signal parameter such as amplitude or phase or frequency.
Conventional oscillating probe mode AFM includes Amplitude Modulation AFM (AM-AFM) which includes tapping mode AFM and multi-frequency AFM, which are in-part illustrated in FIG. 1.
Amplitude Modulation AFM
In amplitude modulation AFM, the feedback input signal measures the RMS (root means squared) amplitude of the probe response signal. Such a signal is denoted as 959P in the illustration in FIG. 1. Using as the feedback input signal the RMS amplitude of the probe response signal and spatially actuating either the probe or the sample towards or away from the other (modulating the distance “D” in FIG. 1) along the z-axis in order to minimize, ideally to zero, the error signal 405P, i.e., the difference between the setpoint signal 375P and the feedback input signal 959P, is the most common type of amplitude modulation AFM (AM-AFM), and illustrated in-part in FIG. 1.
The most commercially successful AFM, tapping mode AFM (e.g., as described in “Tapping Atomic Force Microscope”, U.S. Pat. No. 5,412,980), is an AM-AFM mode. The early and continued success of tapping mode AFM in part led first to the development of other single-frequency AM-AFM modes such as magnetically-actuated probe AFM (U.S. Pat. No. 5,753,814) and more recently to multi-frequency amplitude modulation AFM (commonly called multi-frequency AFM). In multi-frequency AFM, the RMS amplitude feedback input signal 959P may be measured of probe oscillations at select drive frequencies including but also other than the probe's fundamental transverse oscillation resonance frequency (usually called the first eigenfrequency), for example by including one or more lock-in amplifiers in the detector.
Today, however, a technology shift is under way to move away from or to improve upon AM-AFM. Important reasons for this shift are that, 1) as a consequence of tip-sample interaction, probe oscillations often depart from the linear regime, but these important departures are usually relatively small contributors to the probe response signal, which is dominated by oscillations at frequencies (a single frequency or multiple frequencies) driven directly by the probe drive signal; and 2) the departures from linearity frequently occur earlier than substantial relative changes in the probe response signal. Therefore, probe oscillations whole or probe oscillations at frequencies driven directly by the probe drive signal are relatively insensitive to and frequently late in detecting these departures. Consequently, using as the feedback input signal the RMS amplitude of the whole of the detected probe oscillations or of oscillations (possibly at select frequencies) driven directly by the probe drive signal takes into account this non-linearity disproportionately to its significance, and by extension takes into account the source of the nonlinearity, the tip-sample interaction, disproportionately to its significance. Nearly always, the most important operational objective of any AFM is to control the tip-sample interaction. Tip-sample interaction control in AM-AFM, including tapping mode AFM and multi-frequency AFM, limits the fidelity of the images and data produced on a wide range of sample types. Included in these sample types are soft samples, notably many biological samples and soft polymer samples the AM-AFM studies directed to each of which has been a driving force behind the growth of AFM use worldwide so far.
The inadequacies of tip-sample interaction control in AM-AFM are major impediments to further advancement and growth of AFM use and applications in general, because AM-AFM, exemplified by tapping mode AFM and multi-frequency AFM, is still by far the most widespread AFM mode commercially available and in-use everywhere.
Shortcomings of AM-AFM
During raster scanning in AM-AFM, for example in tapping mode AFM and in multifrequency AFM, whenever the probe's sensing tip encounters an increase in sample height, the probe's oscillatory movement is restricted and the amplitude of oscillation and therefore the measured RMS amplitude decrease (e.g., signal 959P decreases). Hereafter, an increase in sample height encountered by the tip is referred to as an up-slope whether it is a gradual increase, a steep increase, or an abrupt increase, i.e., an up-step. Whenever the probe tip encounters a decrease in sample height, gradually or abruptly, the oscillations are less restricted and the RMS amplitude increases (e.g., signal 959P increases). Hereafter, a decrease in sample height encountered by the tip is referred to as a down-slope whether it is a gradual decrease, a steep decrease, or an abrupt decrease; i.e., a down-step. Furthermore, an intrinsically gentle slope, up or down, is effectively encountered by the probe as a steeper slope when the speed of raster scanning (or scan speed) is faster; this point is key to understanding some shortcomings of AM-AFM as will be described herein.
Numerous factors other than the size of the height change encountered by the probe tip and the scan speed affect the change in RMS amplitude in general, that is, on both up-slopes and down-slopes, as well as on relatively flat areas, where height changes are minimal. These factors include but are not limited to the stiffness of the sample and of the probe, and the adhesive, viscoelastic, electric, and magnetic interactions between the sensing tip and the sample. They also include the interaction between the probe tip sidewalls and the sample surface when the probe encounters a surface feature as steep as or steeper than the probe tip sidewalls.
Implicit in interpreting AM-AFM images as topography maps are several assumptions that pertain to down-slopes. One key assumption is that the RMS amplitude increase is proportional to the decrease in sample height. This assumption is generally though not always valid so long as the probe tip does not lose intermittent contact with the sample surface as it scans across the down-slope. Requiring that the probe tip does not lose intermittent contact with the sample surface in turn places an upper limit on the scanning speed in AM-AFM as will be described in detail below.
Furthermore, approximately half of the surface features the probe tip encounters during raster-scanning are down-slopes, half up-slopes. This is because during each and every round trip cycle in raster-scanning, an up-slope during one half of the cycle is usually a down-slope during the subsequent half. This description becomes more accurate as consecutive cycles scan the sample surface more closely to each other; in other words, as the raster scanning covers the scan area with more densely-spaced scan lines (which leads to higher image pixel resolution).
Therefore, approximately half the time the said down-slope scan speed limitation is present (this limitation will be discussed in detail later). Since with rare exceptions the location of a downslope is unknown in advance of the tip encountering it, effectively the speed limitation described here is present nearly one hundred percent of the time during raster scanning in most cases. This is true regardless of sample composition and detail, and regardless of scan area size (image size). This is why this particular speed limitation is a most acute and pervasive problem in search of robust, universally applicable solutions.
Partial solutions to this speed limitation for some targeted applications have been proposed and/or implemented, but the universal nature of this limitation and its continued drag on wider proliferation and use of AFM continuously inspire new solutions; the problem is so pervasive that it has acquired its own well-known name: “parachuting”. In the light of the importance of this speed limitation, the nature and root cause of this imitation will be described in some detail next.
Parachuting, Attendant Speed Limitation, and Small Setpoint Solution
When the oscillating probe's sensing tip encounters a down-slope, the probe is free to oscillate with larger amplitude because the sample surface is less of an obstacle or no obstacle at all to the probe oscillation. In AM-AFM, which uses RMS amplitude of probe oscillations whole or of probe oscillations at frequencies driven directly by the probe drive signal (e.g., 959P in FIG. 1) as feedback input signal, the increase in the RMS amplitude is detected and feedback actuation approaches the probe towards the sample or the sample towards the probe both cases of which are intended to restore the RMS amplitude of probe oscillation such that it remains equal or close to the setpoint signal 375P, thus keeping the error signal 405P at or as close to zero as possible; when this is done successfully, the probe tip is said to track the sample surface.
Scanning across a down-slope at sufficiently fast scan speeds, or at any scan speed but across steep enough down-slopes, or at RMS setpoint values close to the free RMS, which is the value of the RMS amplitude when the probe is far from the sample surface, the sensing tip often loses intermittent contact with the sample surface during several consecutive oscillation cycles; the sensing tip does not reach the sample surface because, as the probe is scanned along the down-slope, even with the action of the feedback (z-) actuator 700P taken into account, the separation at the bottom of each oscillation cycle (i.e., at the point of closest approach) between the probe tip and the sample surface increases faster than do the amplitude and the RMS amplitude of probe oscillations whole and of probe oscillations at frequencies driven directly by the probe drive signal; the feedback input signal 959P fails to increase fast enough to faithfully reflect the increased separation between the probe tip and the sample surface. If this failure continues, eventually the RMS amplitude grows to its maximum value, the free RMS, and the error signal 405P is said to be saturated.
As a consequence of this failure (with or without the error signal saturated), the error signal 405P, and ultimately the feedback output signal 1089P no longer accurately represent changes of sample topography. The probe no longer tracks the sample surface. This is parachuting, illustrated in FIG. 2A. Parachuting is a common problem in AM-AFM, for example in tapping mode and in multi-frequency AFM, and afflicts imaging applications of AFM across the board; it does not depend on sample type; and it happens in gaseous and liquid environments as well as in vacuum.
Three points deserve attention in regards to parachuting: 1) Parachuting arises not only when the probe tip encounters a genuinely steep down-slope, but also when the scanning speed is fast enough so that even a gentle down-slope effectively becomes a steep down-slope. Herein lays a key connection to the aforementioned parachuting-related scan speed limitation of AM-AFM, not only in scanning ragged and highly irregular surfaces, but also in scanning smooth surfaces largely devoid of sharp discontinuities. Therefore, the phrase “steep down-slope” is to be understood in this context: a slope that is either in reality steep or a slope that may not be steep, but effectively becomes steep when the scan speed is fast enough. Furthermore, “fast enough” is not necessarily fast at all. Parachuting is often a problem when operating an AM-AFM at scan speeds as low as 1 micrometer a second. 2) The closer is the RMS amplitude setpoint signal 375P to the free RMS amplitude, i.e., the RMS amplitude when the tip and sample are far apart, the more likely is parachuting. In other words, for a given free RMS amplitude, the larger is the setpoint signal 375P value in AM-AFM, the more likely is parachuting. 3) On the other hand, in general, for a given free RMS amplitude, a larger setpoint signal 375P value means a relatively gentler tip-sample intermittent contact in AM-AFM (lighter tapping), and this is frequently desirable as sample damage and/or tip deformation is less likely with gentler tip-sample intermittent contact.
One approach to limit or avoid parachuting in AM-AFM is to set the setpoint signal 375P value small. The resulting stronger intermittent contact forces (harder tapping) are detrimental to many samples, notably softer samples including many biological samples and many polymer samples. If sample deformation under the harder tapping tip is not permanent because of the sample's elasticity, then the image data is misrepresentative of the sample surface height. If the sample is harder than the tip, then the detriment is to the tip which becomes dull with harder tapping and image resolution suffers. This brute-force approach (reducing the setpoint signal value and thereby increasing tapping force) to limit or eliminate parachuting is even more detrimental to the sample surface (or to the tip) when used in combination with fast scanning speeds. Unfortunately, this combination, lower setpoint and faster scanning speed, is frequently used especially by users insufficiently familiar with the ways in which tip-sample interaction control is affected by the interrelations between setpoint value, scanning speed, feedback gains, and other control parameters in AM-AFM.
Probe Q and Parachuting
The duration of parachuting is determined by several factors. These include scan speed, feedback gains, RMS setpoint, free RMS value, and of course the inherent steepness of the down-slope (which by our definition includes the height of a down-step). Excluding the inherent steepness of the down-slope, many of these factors are subject to human operator control.
For a given set of human-operator-controlled parameters, during parachuting, when intermittent contact between the sensing tip and the sample is lost, the speed at which the probe oscillation amplitude and therefore RMS amplitude of probe oscillations whole and of probe oscillations at frequencies driven directly by the probe response signal grow is determined in part by the quality factor, Q, of the resonance(s) at or near to whose frequency or frequencies the AM-AFM probe is driven by the probe drive signal. The higher the Q, the slower is the amplitude build-up, and the longer is the time during which the sensing tip fails to reach the sample surface at the bottom of successive oscillation cycles before it finally succeeds. In other words, the higher is the Q, the longer is the duration of parachuting. During parachuting in AM-AFM, the RMS amplitude of probe oscillation whole or of probe oscillations at frequencies driven directly by the probe drive signal (e.g., 959P) grows too slowly to maintain intermittent tip-sample contact even as the distance “D” in FIG. 1 between the sample stage 800P and the probe base 2P is decreased with AM-AFM's z-actuator 700P feedback action. The RMS amplitude 959P of the probe response signal 59P and therefore the error signal 405P of the feedback loop fail to accurately and in a timely fashion reflect the change of sample height passing under the scanning probe's tip as raster-scanning proceeds. If the RMS amplitude setpoint signal 375P value is close to the value of free RMS amplitude, the error signal 405P saturates at its maximum value and exacerbates this problem, leading in turn to even longer parachuting times.
As a result, the output of the feedback loop which is ultimately the actuation of the probe towards the sample (or the sample towards the probe) also fails to represent the change of sample height (or topography). (We recall that the height or topography image is built pixel by pixel on the output of the feedback loop, i.e., on 1089P). The portions of an image constructed from the feedback output signal during the times when the probe parachutes down to the sample surface, rather than track the sample surface with intermittent contact, appear as smooth, gradual slopes; these portions of the image are entirely artifact.
Conventional Approaches to Parachuting and Down-slope Speed Limitation
Besides using smaller RMS amplitude setpoint, one way to address the problem of parachuting is to use AFM probes that have higher eigenfrequencies or resonant frequencies, including the lowest eigenfrequency. For a given value of the Q, if the probe oscillation frequency (at or near the corresponding resonance) is higher, then the amplitude builds up faster, alleviating the described down-slope speed limitation. As far back as 1996, this approach has been applied, mainly for imaging biological samples, and frequently in a liquid environment (“Short cantilevers for atomic force microscopy”; D. A. Walters1, J. P. Cleveland1, N. H. Thomson1, P. K. Hansma1, M. A. Wendman2, G. Gurley2 and V. Elings; Rev. Sci. Instrum. 67, 3583 (1996)). Probes with frequencies in the mega Hertz (MHz) range have been introduced. This approach has been successful in some applications. For example, extremely smooth biological surfaces with feature heights only in nanometers have been successfully imaged in liquid very fast. One limitation here is the requirement that the sample surface be smooth (T. Uchihashi and T. Ando, “Atomic Force Microscopy in Biomedical Research”, Methods in Molecular Biology Volume 736, pp 285-300, 2011). Another limitation of this approach appears to be that the sample be imaged in liquid.
Regardless of applications, and notwithstanding its success where it has been documented, some limitations of this approach are 1) the required cantilever probes tend to be difficult to use because of their unusually small size even by micro-fabrication standards applicable to AFM probes; 2) optical and mechanical engineering and components required to implement the monitoring of smaller cantilever's movement are demanding, adding to system complexity and cost (see, e.g., T. Uchihashi and T. Ando, “Atomic Force Microscopy in Biomedical Research”, Methods in Molecular Biology Volume 736, pp 285-300, 2011; and J. D. Adams et al., “High-speed imaging upgrade for a standard sample scanning atomic force microscope using small cantilevers”, Review of Scientific Instruments, volume 85, 093702, 2014”); and 3) larger cantilevers of this type (high frequency) tend to be quite stiff, lacking the required force sensitivity to be used to probe soft samples; therefore they damage soft samples.
Another solution to the parachuting problem is to engineer a Q-control routine so as to intentionally reduce the effective Q of the AFM probe, thereby alleviating parachuting and the associated scan speed limitation on downslopes. When the effective Q is reduced, oscillation amplitude builds up faster on a down-slope, and tip-sample intermittent contact is re-established sooner. (“High-speed tapping mode imaging with active Q control for atomic force microscopy”, T. Sulchek, et. al, Applied Physics Letters Volume 76, Number 11, 13; March 2000, pp. 1473-1475.) This has been done with even less success than the higher-frequency cantilever approach. The proof of the limitation of this approach is best evident in the fact that beyond a single exception (measuring laser zone textured (LZT) magnetic hard drives sometime in the early 2000's) the technique did not and has not achieved any measurable success in the marketplace to address the down-slope speed limitation on any type of sample; it has not been widely adopted as a solution to this speed limitation despite the fact that the speed limitation it had intended to address is universal, as described earlier.
False Engages in AM-AFM
AM-AFM uses the RMS amplitude 959P of the probe response signal 59P as the input signal to the feedback scheme; this quantity gradually decreases when the AFM probe approaches the sample surface during a pre-engage sequence including the initial approach prior to initial engage. This decrease is mainly due to the additional fluid-dynamic damping of the probe by some of the fluid which engulfs the probe becoming partially trapped between the body of the oscillating probe and the sample surface during approach. Probe oscillations are always damped by the fluid in which the probe oscillates, but when the probe-sample distance becomes comparable to the smaller of the probe's two planar dimensions (e.g., the width of a cantilever probe), the damping becomes stronger, and in some cases an additional spring-like effect also appears which makes the probe effectively stiffer than it actually is. These phenomena are collectively called squeeze-film effect and are frequently relevant to AFM operation in an oscillating probe mode. (“Air-Damping of AFM Micro-Cantilevers in the Presence of a Nearby Surface,” F M Serry, P Neuzil, R Vilasuso, and G J Maclay in Proceedings of The 188th Electrochemical Society National Symposium, Chicago, Ill., 1995.)
During the final stages of an approach, the reduction of the RMS amplitude as a consequence of squeeze-film damping frequently results in “false-engage” events. The AM-AFM feedback scheme treats the squeeze-film damping-induced reduction of the RMS amplitude as if it were due to tip-sample intermittent contact, (which is false); the AFM false-engages, and starts raster scanning and producing an image which is comprised totally of artifact. A solution to the problem of false-engage in AM-AFM was developed early on by the developers of tapping mode AFM. In this scheme, in summary, when the RMS amplitude drops, the feedback scheme halts the approach, then reduces the setpoint incrementally. If the feedback output adjusts incrementally, then the engage is deemed to be real and raster scanning commences. If on the other hand the feedback output adjusts largely, then the engage is aborted (it is false); the approach continues. In the art, the scheme is referred to as “sewing”, because with each iteration, except possibly the last, there is also a pull-back of the actuator; but the basic scheme is as described. Sewing largely reduces incidents of false engage, especially in gaseous environments. The price the user pays for this solution is a long wait time during the approach. It is common to have a sewing engage sequence of 5-7 minutes; a 3-minute wait is very common. Given that frequently when a user wants to examine different locations on the sample surface (s)he has to engage, withdraw, and re-engage the probe several times in an hour, the cumulative waiting time is often painfully long, but absent a robust solution, this waiting time is accepted as a necessary nuisance to deal with false engages.
In liquids, however, sewing sometimes does not work. Sometimes a sewing step never completes; the feedback scheme is suspended without any action as the implementation of the sewing algorithm fails to resolve one way or another: real engage, or false engage. Much of this is due to the complicated ways in which the laser light which is to probe the movement of the cantilever alters its trajectory and intensity as it traverses across several media: air, liquid, possibly air bubbles in the liquid, and the glass or clear polymer (sometimes including optical coatings) that makes up the AFM fluid cell (also called the liquid cell). In these cases, the operator is forced to manually make some type of adjustment, either in hardware or in software or in both. The adjustments sometimes include completely disassembling and re-assembling the fluid cell, which is very time-consuming, and requires both patience and dexterity. In short, sewing can and too often does fail when operating AM-AFM with a fluid cell.
False engages can also occur when a sample's surface is highly reflective of light. In these situations, various optical effects that involve a laser light beam such as used in an optical detection scheme trigger a false engage with and/or without the use of a fluid cell.
To summarize: with recent advances in theoretical and computational science of oscillating probe mode AFM including AM-AFM and with growing body of experimental verifications, change of the RMS amplitude of probe oscillations at frequencies driven directly by the probe drive signal as reflected in the change of the RMS amplitude of the probe response signal is frequently no longer considered a reliable enough indicator of the change in the interaction between the probe tip and the sample surface on many sample types. For example, parachuting and the resulting scanning speed limitation, lack of acceptable image fidelity, and false engages may result in inadequate, inaccurate, and/or time consuming AFM measurements. For many years AM-AFM, exemplified mainly by tapping mode AFM, which uses RMS amplitude of the probe response signal as feedback input signal, has been a driving force behind the growth of AFM and its application space. If, in conventional AFM including AM-AFM including tapping mode AFM, the speed limitations (including during approach and during raster scanning), inadequate tip-sample interaction control, and the attendant compromised image fidelity were addressed robustly and applicably to a wide range of samples, then the adoption of AFM as a desirable surface metrology and analysis instrument across industries and applications would very likely have proceeded even faster than it has been and that it is going to be with these problems lingering.